Device for continuous glass thickness determination

Translated from Steklo i Keramika, No. 5, pp. 23–24, May, 1990.     

Application of radio frequency method to measurements in cryogenics

This paper reports the specific features of the radio frequency method used to measure characteristics of cryogenic flows. The techniques for determination of the void fraction and quality of two-phase flows and the mean integral thermodynamic characteristics of single-phase flows, e.g. temperature and density, are described. The design and basic parameters of sensors with channels of round and annular cross-section are discussed. Possible combinations of these sensors with other devices for the measurement of two-phase and single-phase medium flow rates are shown. Information about the measuring system as well as measurement results for helium and nitrogen are presented. The sensor characteristics for hydrogen and methane have been estimated theoretically.     

Ab initio calculations of phonon dispersion in CdGa<Subscript>2</Subscript>Se<Subscript>4</Subscript>

The density of phonon states and the phonon dispersion in the Brillouin zone are calculated by the density functional method of. The displacements of atoms in the elementary cell are constructed for vibrations of the A, B, and E symmetries. The calculated frequencies of optical phonons are consistent with the experimentally determined frequencies from the IR-absorption (infrared) and Raman-scattering spectra. In the xy plane, the intersection of low-frequency optical phonons with acoustic phonons is observed.     

Equations for determining the thermodiffusion ratio of a binary gas mixture

Differential equations describing the temperature and concentration dependence of the thermodiffusion ratio for binary gas mixtures and saturated vapor-gas mixtures are derived on the basis of linear phenomenological equations for the total molecular flux of mass and heat.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 50, No. 6, pp. 989–996, June, 1986.     

Accurate evaluation of integrals arising from the bulk electron densities in quantum wells of high electron mobility transistors

In this paper we propose a new accurate approach to compute integrals arrays of the electron density and energy density in a multi-layered high electron mobility transistors (HEMTs) device. These new formulas enable the user to calculate efficiently the certain integrals. Example results on the simulation of a certain integrals are given to demonstrate the efficiency of the new scheme. The results are compared with other theoretical calculation results. The convergence rate of the series is estimated and discussed.     

Exact analytical expressions and numerical analysis of two-center Franck-Condon factors and matrix elements over displaced harmonic oscillator wave functions

A detailed study is undertaken, using various techniques, in deriving analytical formula of Franck-Condon overlap integrals and matrix elements of various functions of power (xl), exponential (exp(−2cx)) and Gaussian (exp(−cx²)) over displaced harmonic oscillator wave functions with arbitrary frequencies. The results suggested by previous experience with various algorithms are presented in mathematically compact form and consist of generalization. The relationships obtained are valid for the arbitrary values of parameters and the computation results are in good agreement with the literature. The numerical results illustrate clearly a further reduction in calculation times.

Program summary

Program name:FRANCKCatalogue identifier:ADXX_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXX_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandProgramming language:Mathematica 5.0Computer:Pentium M 1.4 GHzOperating system:Mathematica 5.0RAM:512 MBNo. of lines in distributed program, including test data, etc.:825No. of bytes in distributed program, including test data, etc.:16 344Distribution format:tar.gzNature of problem:The programs calculate the Franck-Condon factors and matrix elements over displaced harmonic oscillator wave functions with arbitrary quantum numbers (n,n₁), frequencies (a,a₁) and displacement (d) for the various functions of power (xl), exponential (exp(−2cx)) and Gaussian (exp(−cx²)).Solution method:The Franck-Condon factors and matrix elements are evaluated using binomial coefficients and basic integrals.Restrictions:The results obtained by the present programs show great numerical stability for arbitrary quantum numbers (n,n₁), frequencies (a,a₁) and displacement (d).Unusual features:NoneRunning time:As an example, for the value of Franck-Condon Overlap Integral Inn^′(d;α,α^′)=0.004405001887372332 with n=3, n₁=2, a=4, a₁=3, d=2, the compilation time in a Pentium M 1.4 GHz computer is 0.18 s. Execution time depends on the values of integral parameters n, n^′, d, α, α^′.